Reference problem ===================== Geometry --------- .. image:: images/Object_1.svg :width: 319 :height: 159 .. _RefImage_Object_1.svg: Material properties ------------------------ Isotropic elasticity :math:`E\mathrm{=}2.{E}^{11}\mathit{Pa}` :math:`\nu =0.3` Viscoplasticity model VISCOCHAB (modeling A), without kinematic work hardening: .. csv-table:: ":math:`k` "," :math:`626.423911{E}^{6}\mathit{Pa}` "," :math:`\text{Q\_M}` "," "," :math:`3.982809551{E}^{8}\mathit{Pa}` "," :math:`\text{C2}` ", "0" ":math:`\text{A\_K}` "," :math:`0.215443469` "," :math:`\text{Q\_0}` "," "," :math:`3.982809551{E}^{8}\mathit{Pa}` "," :math:`\text{C1}` ", "0" ":math:`\text{B}` "," :math:`11.53016` "," :math:`\text{K\_0}` "," "," :math:`k\mathrm{\times }0.21544\mathit{Pa}{S}^{1\mathrm{/}N}` "," :math:`\text{G1\_0}` ", "0" "", "", ":math:`\text{N}` ", "12"," :math:`\text{G2\_0}` ", "0" Elasto-plasticity with isotropic work hardening (B modeling): model VMIS_ISOT_TRAC +----------------------------------------+---------------------------------+--------------+----------------------------------+ |Isotropic work hardening | | +----------------------------------------+---------------------------------+--------------+----------------------------------+ |:math:`\text{R\_0}\mathrm{=}\mathit{Sy}`|:math:`750\mathit{E⁶}\mathit{Pa}`| | | +----------------------------------------+---------------------------------+--------------+----------------------------------+ |Traction curve | | +----------------------------------------+---------------------------------+--------------+----------------------------------+ |:math:`{\epsilon }_{0}` |:math:`\mathit{Sy}\mathrm{/}E` |:math:`\sigma`|:math:`\mathit{Sy}` | +----------------------------------------+---------------------------------+--------------+----------------------------------+ |:math:`\epsilon` | |:math:`\sigma`|:math:`1500\mathit{E⁶}\mathit{Pa}`| +----------------------------------------+---------------------------------+--------------+----------------------------------+ Viscoplasticity (C modeling): model VISC_ISOT_TRAC +----------------------------------------+----------------------------------+--------------+----------------------------------------+ |Isotropic work hardening | | +----------------------------------------+----------------------------------+--------------+----------------------------------------+ |:math:`\text{R\_0}\mathrm{=}\mathit{Sy}`|:math:`750\mathit{E⁶}\mathit{Pa}` | | | +----------------------------------------+----------------------------------+--------------+----------------------------------------+ |VISC_SINH | +----------------------------------------+----------------------------------+--------------+----------------------------------------+ |:math:`\text{SIGM\_0}` |:math:`6167\mathrm{E⁶}\mathrm{Pa}`|EPSI_0 |:math:`3.31131121483{E}^{13}\mathit{Pa}`| +----------------------------------------+----------------------------------+--------------+----------------------------------------+ |:math:`\text{M}` |:math:`6.76` | | | +----------------------------------------+----------------------------------+--------------+----------------------------------------+ |Traction curve | +----------------------------------------+----------------------------------+--------------+----------------------------------------+ |:math:`{\epsilon }_{0}` |:math:`\mathit{Sy}\mathrm{/}E` |:math:`\sigma`|:math:`\mathit{Sy}` | +----------------------------------------+----------------------------------+--------------+----------------------------------------+ |:math:`\epsilon` | |:math:`\sigma`|:math:`1500\mathrm{E⁶}\mathrm{Pa}` | +----------------------------------------+----------------------------------+--------------+----------------------------------------+ Material settings under CRIT_RUPT: Critical constraint: :math:`\text{SIGMA\_C}\mathrm{=}7.8{E}^{8}\mathit{Pa}`, :math:`\mathit{COEF}\mathrm{=}10000.` :ref:`[4] ` Boundary conditions and loads ------------------------------------- +----------------------------------+----------------------------+-----------------------------------------------------------------------------------+--------------------------------------------++ |Imposed deformation: || +----------------------------------+----------------------------+-----------------------------------------------------------------------------------+--------------------------------------------++ |:math:`{\epsilon }_{\mathrm{max}}`|:math:`0.05` |speed |:math:`{1.E}^{-4}` || +----------------------------------+----------------------------+-----------------------------------------------------------------------------------+--------------------------------------------++ |Time-dependent charging: || +----------------------------------+----------------------------+-----------------------------------------------------------------------------------+--------------------------------------------++ |:math:`{t}_{0}\mathrm{=}0.` |:math:`\epsilon \mathrm{=}0`|:math:`\mathit{tmax}\mathrm{=}` :math:`{\epsilon }_{\mathrm{max}}/\mathrm{vitesse}`|:math:`\epsilon ={\epsilon }_{\mathrm{max}}`|| +----------------------------------+----------------------------+-----------------------------------------------------------------------------------+--------------------------------------------++ .. csv-table:: "Traction:", ":math:`\mathit{FACEYZ}` "," :math:`\mathrm{Dz}=1` ", "" .. csv-table:: "Blocking:", ":math:`\mathit{FACEXZ}` :math:`\mathrm{Dy}=0` "," :math:`\mathrm{FACEXY}` "," :math:`\mathrm{Dz}=0`" "", "", ":math:`\mathrm{FACEYZ}` "," :math:`\mathrm{Dx}=0`"